Prediction Model for Income Classification
Under $50000 vs Over $50000
steve dubois
4/22/2019
ABSTRACT
The prominent inequality of wealth and income is a huge concern especially in the United States. The likelihood of diminishing poverty is one valid reason to reduce the world’s surging level of economic inequality. The principle of universal moral equality ensures sustainable development and improves the economic stability of a nation. Governments in different countries have been trying their best to address this problem and provide an optimal solution. The aim here to show the usage of machine learning techniques in providing a solution to the income equality problem. The UCI Adult Dataset has been used for the purpose. Specifically, several machine learning classification models have been compared to predict whether a person’s yearly income in the US falls in the income category of either greater than 50K dollars or less/equal to 50K dollars category based on a certain set of attributes. So, what_Y(>50, <=50) is predicted given (X1, X2, X3,…Xn), where Y is an income level, and X is a statistic feature of an individual.
LIBRRARIES USED - R PACKAGES
library(knitr)
library(ggvis)
library(ISLR)
library(e1071)
library(gmodels)
library(tidyverse)
library(tidyr)
library(dplyr)
library(readr)
library(ggplot2)
library(randomForest)
library(caret)
library(data.table)
library(gbm)
library(rpart)
library(rpart.plot)
library(plotly)
library(ggvis)
library(neuralnet)
library(nnet)
library(MASS)
library(devtools)
install_github('araastat/reprtree', force = TRUE)##
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## library(reprtree)
library(rattle)
library(NeuralNetTools)LOADING CENSUS DATA
url.train <- "http://archive.ics.uci.edu/ml/machine-learning-databases/adult/adult.data"
url.test <- "http://archive.ics.uci.edu/ml/machine-learning-databases/adult/adult.test"
url.names <- "http://archive.ics.uci.edu/ml/machine-learning-databases/adult/adult.names"
download.file(url.train, destfile = "adult_train.csv")
download.file(url.test, destfile = "adult_test.csv")
download.file(url.names, destfile = "adult_names.txt")
# Read the training and test data into memory
train <- read.csv("adult_train.csv", header = FALSE)
# The test data has an unnecessary first line that messes stuff up, this fixes that problem
all_content <- readLines("adult_test.csv")
skip_first <- all_content[-1]
test <- read.csv(textConnection(skip_first), header = FALSE)Initializing headers
feature <- c("Age","Work_Class", "Final_Weight", "Education", "Education_Num", "Marital_Status", "Occupation", "Relationship", "Race", "Sex", "Capital_Gain", "Capital_Loss", "Hours_Per_Week", "Native_Country", "IncomeCLASS")##
## TRUE
## 32561##
## Under_50K More_50K
## 76 24## [1] 0## [1] 0LINEAR DISCRIMINANT ANALYSIS
Identification the Signigicant Demographic Feaures
set.seed(1414)
model.lda <- train(IncomeCLASS ~ .,
data = train,
method = "lda")RANKING FEATURE SIGNIFICANCE TO INCOME CLASSS
plot(varImp(model.lda))
SETTING CATEGORICAL; FEATURES
EXPLORATORY DATA ANALYSIS USING GGPLOT
P <- ggplot(train,aes(x = Age, fill = IncomeCLASS)) + geom_bar(position = "fill", color = "black") + coord_flip() + theme(axis.text = element_text(colour = "darkred", size = rel(0.75), angle = 45))
P1 <- P + labs(title = "Age vs Income Class Proportion")
ggplotly(P1 = ggplot2::last_plot())gg <- train %>% ggvis(x = ~Age) %>% layer_histograms(fill = "green")
ggQ <- ggplot(train,aes(x = Education, fill = IncomeCLASS)) + geom_bar() + coord_flip()
Q1 <- Q + labs(title = "Education vs Income Class Proportion") + theme(axis.text = element_text(colour = "darkred", size = rel(0.75), angle = 45))
ggplotly(Q1 = ggplot2::last_plot())train %>% ggvis(x = ~Age) %>% layer_histograms() %>% layer_paths( strokeWidth := 1, stroke := "red")R <- train %>% ggplot(aes(x = Work_Class, fill = IncomeCLASS)) + geom_bar(position = "fill", color = "black") + theme(axis.text = element_text(colour = "darkred", size = rel(0.75), angle = 45))
R1 <- R + labs(title = "Work_Class vs Income Class Proportion")
ggplotly(R1 = ggplot2::last_plot())We find that the people employed in private companies have more people with income above 50k and Self Employed people having a higher proportion of peoplw with income greater than 50k.
hh <- train %>% ggvis(x = ~Education_Num) %>% layer_histograms(fill = "green")
hhS <- ggplot(train,aes(x = Education_Num, fill = IncomeCLASS)) + xlab("Years of Education") + ylab("proportion within category") + geom_bar(color = "black") + coord_flip() + theme(axis.text = element_text(colour = "darkred", size = rel(0.75), angle = 45))
S1 <- S + labs(title = "Length of Eduction VS Income Class Proportion")
ggplotly(S1 = ggplot2::last_plot())T <- ggplot(train,aes(x = Relationship, fill = IncomeCLASS)) + ggtitle("Relationship VS Income Class Proportion") + xlab("Relationship") + ylab("proportion within category") + geom_bar(position = "fill", color = "black") + coord_flip() + theme(axis.text = element_text(colour = "darkred", size = rel(0.75), angle = 45))
T1 <- T + labs(title = "Relationship vs Income Class Proportion")
ggplotly(T1 = ggplot2::last_plot())jj <- ggplot(train,aes(x = Occupation, fill = IncomeCLASS)) + ggtitle("Occupation VS Income Class Proportion") + xlab("Occupation") + ylab("proportion within category") + geom_bar(position = "fill", color = "black") + coord_flip() + theme(axis.text = element_text(colour = "darkred", size = rel(0.75), angle = 45))
ggplotly(jj = ggplot2::last_plot())PERFORMANCE METRICS for PREDICTIVE POWER DETERMINATION & MODEL SELECTION:
Accuracy Statistic: The higher, the better. (0:1)
Accuracy defined more simply: # of correction predictions / total predictions
Accuracy defined in terms of true positives/negatives: TN + FN / # SAMPLES
Kappa Statistic: The higher, the better. (0:1)
NAIVE BAYES MODEL
#train Naive Bayes
set.seed(32323)
model_Naive <- naiveBayes(IncomeCLASS ~ ., data = train)
pred_Nb <- predict(model_Naive, test)
levels(train$IncomeCLASS) <- c("Under_50K", "More_50K")
levels(test$IncomeCLASS) <- c("Under_50K", "More_50K")
levels(pred_Nb) <- c("Under_50K", "More_50K")
confusionMatrix(pred_Nb, test$IncomeCLASS)## Confusion Matrix and Statistics
##
## Reference
## Prediction Under_50K More_50K
## Under_50K 11567 1978
## More_50K 868 1868
##
## Accuracy : 0.8252
## 95% CI : (0.8193, 0.831)
## No Information Rate : 0.7638
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.4619
## Mcnemar's Test P-Value : < 2.2e-16
##
## Sensitivity : 0.9302
## Specificity : 0.4857
## Pos Pred Value : 0.8540
## Neg Pred Value : 0.6827
## Prevalence : 0.7638
## Detection Rate : 0.7105
## Detection Prevalence : 0.8320
## Balanced Accuracy : 0.7079
##
## 'Positive' Class : Under_50K
## CrossTable(pred_Nb, test$IncomeCLASS)##
##
## Cell Contents
## |-------------------------|
## | N |
## | Chi-square contribution |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 16281
##
##
## | test$IncomeCLASS
## pred_Nb | Under_50K | More_50K | Row Total |
## -------------|-----------|-----------|-----------|
## Under_50K | 11567 | 1978 | 13545 |
## | 144.270 | 466.457 | |
## | 0.854 | 0.146 | 0.832 |
## | 0.930 | 0.514 | |
## | 0.710 | 0.121 | |
## -------------|-----------|-----------|-----------|
## More_50K | 868 | 1868 | 2736 |
## | 714.229 | 2309.267 | |
## | 0.317 | 0.683 | 0.168 |
## | 0.070 | 0.486 | |
## | 0.053 | 0.115 | |
## -------------|-----------|-----------|-----------|
## Column Total | 12435 | 3846 | 16281 |
## | 0.764 | 0.236 | |
## -------------|-----------|-----------|-----------|
##
## summary(pred_Nb)## Under_50K More_50K
## 13545 2736cm_Nb <- data.frame(confusionMatrix(pred_Nb, test$IncomeCLASS)[3])
kable(cm_Nb)| overall | |
|---|---|
| Accuracy | 0.8251950 |
| Kappa | 0.4619397 |
| AccuracyLower | 0.8192724 |
| AccuracyUpper | 0.8310012 |
| AccuracyNull | 0.7637737 |
| AccuracyPValue | 0.0000000 |
| McnemarPValue | 0.0000000 |
TRAIN THE RPART DECISION TREE MODEL
# rpart decision tree
set.seed(32323)
model_part <- caret::train(IncomeCLASS ~ ., data = train, method = "rpart")
pred_rpart <- predict(model_part, test, type = "raw")
confusionMatrix(pred_rpart, test$IncomeCLASS)## Confusion Matrix and Statistics
##
## Reference
## Prediction Under_50K More_50K
## Under_50K 11808 2042
## More_50K 627 1804
##
## Accuracy : 0.8361
## 95% CI : (0.8303, 0.8417)
## No Information Rate : 0.7638
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.4796
## Mcnemar's Test P-Value : < 2.2e-16
##
## Sensitivity : 0.9496
## Specificity : 0.4691
## Pos Pred Value : 0.8526
## Neg Pred Value : 0.7421
## Prevalence : 0.7638
## Detection Rate : 0.7253
## Detection Prevalence : 0.8507
## Balanced Accuracy : 0.7093
##
## 'Positive' Class : Under_50K
## cm_rpart <- data.frame(confusionMatrix(pred_rpart, test$IncomeCLASS)[3])
CrossTable(pred_rpart, test$IncomeCLASS)##
##
## Cell Contents
## |-------------------------|
## | N |
## | Chi-square contribution |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 16281
##
##
## | test$IncomeCLASS
## pred_rpart | Under_50K | More_50K | Row Total |
## -------------|-----------|-----------|-----------|
## Under_50K | 11808 | 2042 | 13850 |
## | 142.958 | 462.215 | |
## | 0.853 | 0.147 | 0.851 |
## | 0.950 | 0.531 | |
## | 0.725 | 0.125 | |
## -------------|-----------|-----------|-----------|
## More_50K | 627 | 1804 | 2431 |
## | 814.465 | 2633.353 | |
## | 0.258 | 0.742 | 0.149 |
## | 0.050 | 0.469 | |
## | 0.039 | 0.111 | |
## -------------|-----------|-----------|-----------|
## Column Total | 12435 | 3846 | 16281 |
## | 0.764 | 0.236 | |
## -------------|-----------|-----------|-----------|
##
## summary(pred_rpart)## Under_50K More_50K
## 13850 2431kable(cm_rpart)| overall | |
|---|---|
| Accuracy | 0.8360666 |
| Kappa | 0.4795717 |
| AccuracyLower | 0.8302892 |
| AccuracyUpper | 0.8417236 |
| AccuracyNull | 0.7637737 |
| AccuracyPValue | 0.0000000 |
| McnemarPValue | 0.0000000 |
accuracy <- sum(pred_rpart == test$IncomeCLASS)/length(test$IncomeCLASS)
print(accuracy)## [1] 0.8360666rpart.plot(model_part$finalModel)
TRAIN THE RANDOM FOREST MODEL
set.seed(32323)
model.rf <- randomForest(IncomeCLASS ~ ., data = train, ntree = 500, importance = TRUE, mtry = 2, do.trace = 100)## ntree OOB 1 2
## 100: 13.40% 5.93% 36.95%
## 200: 13.35% 5.86% 36.99%
## 300: 13.30% 5.81% 36.88%
## 400: 13.31% 5.87% 36.79%
## 500: 13.34% 5.94% 36.67%pred.rf <- predict(model.rf, test)
summary(pred.rf)## Under_50K More_50K
## 13107 3174reprtree:::plot.getTree(model.rf, k = 3, depth = 4)
confusionMatrix(test$IncomeCLASS, pred.rf)## Confusion Matrix and Statistics
##
## Reference
## Prediction Under_50K More_50K
## Under_50K 11670 765
## More_50K 1437 2409
##
## Accuracy : 0.8648
## 95% CI : (0.8594, 0.87)
## No Information Rate : 0.805
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.6011
## Mcnemar's Test P-Value : < 2.2e-16
##
## Sensitivity : 0.8904
## Specificity : 0.7590
## Pos Pred Value : 0.9385
## Neg Pred Value : 0.6264
## Prevalence : 0.8050
## Detection Rate : 0.7168
## Detection Prevalence : 0.7638
## Balanced Accuracy : 0.8247
##
## 'Positive' Class : Under_50K
## cm.rf <- data.frame(confusionMatrix(pred.rf, test$IncomeCLASS)[3])
kable(cm.rf)| overall | |
|---|---|
| Accuracy | 0.8647503 |
| Kappa | 0.6011184 |
| AccuracyLower | 0.8594013 |
| AccuracyUpper | 0.8699687 |
| AccuracyNull | 0.7637737 |
| AccuracyPValue | 0.0000000 |
| McnemarPValue | 0.0000000 |
NEURAL NETWORKS
set.seed(32323)
keeps <- c("Education_Num",
"Age",
"Hours_Per_Week",
"Sex",
"Capital_Gain",
"IncomeCLASS")
train.reduced <- train[,which(names(train) %in% keeps)]
test.reduced <- test[,which(names(test) %in% keeps)]
start <- proc.time()[3]
model.nn <- train(IncomeCLASS ~ .,
data = train.reduced,
method = "nnet")par(mar = c(1, 1, 1, 1))
plotnet(model.nn$finalModel, y_names = "IncomeCLASS")
title("Graphical Representation of our Neural Network")
predictions <- predict(model.nn, test.reduced[,1:5])
accuracy <- sum(predictions == test.reduced[,6])/length(test.reduced[,6])
print(accuracy)
cm.neural <- data.frame(confusionMatrix(predictions, test.reduced$IncomeCLASS)[3])
kable(cm.neural)
garson(model.nn$finalModel)
## Confusion Matrix and Statistics
##
## Reference
## Prediction Under_50K More_50K
## Under_50K 11062 1373
## More_50K 1165 2681
##
## Accuracy : 0.8441
## 95% CI : (0.8384, 0.8497)
## No Information Rate : 0.751
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.5759
## Mcnemar's Test P-Value : 3.976e-05
##
## Sensitivity : 0.9047
## Specificity : 0.6613
## Pos Pred Value : 0.8896
## Neg Pred Value : 0.6971
## Prevalence : 0.7510
## Detection Rate : 0.6794
## Detection Prevalence : 0.7638
## Balanced Accuracy : 0.7830
##
## 'Positive' Class : Under_50K
## | overall | |
|---|---|
| Accuracy | 0.8441128 |
| Kappa | 0.5759170 |
| AccuracyLower | 0.8384486 |
| AccuracyUpper | 0.8496537 |
| AccuracyNull | 0.7637737 |
| AccuracyPValue | 0.0000000 |
| McnemarPValue | 0.0000398 |
| overall | |
|---|---|
| Accuracy | 0.8441128 |
| Kappa | 0.5759170 |
| AccuracyLower | 0.8384486 |
| AccuracyUpper | 0.8496537 |
| AccuracyNull | 0.7637737 |
| AccuracyPValue | 0.0000000 |
| McnemarPValue | 0.0000398 |
MODEL COMPARISON
NAIVE BAYES
kable(cm_Nb)| overall | |
|---|---|
| Accuracy | 0.8251950 |
| Kappa | 0.4619397 |
| AccuracyLower | 0.8192724 |
| AccuracyUpper | 0.8310012 |
| AccuracyNull | 0.7637737 |
| AccuracyPValue | 0.0000000 |
| McnemarPValue | 0.0000000 |
RPART
kable(cm_rpart)| overall | |
|---|---|
| Accuracy | 0.8360666 |
| Kappa | 0.4795717 |
| AccuracyLower | 0.8302892 |
| AccuracyUpper | 0.8417236 |
| AccuracyNull | 0.7637737 |
| AccuracyPValue | 0.0000000 |
| McnemarPValue | 0.0000000 |
NEURAL NETWORK
#### NEURAL MODEL >>> model_neural_AA <- train(IncomeCLASS ~ ., data = train, method = “nnet”, trControl =
RANDOM FOREST
kable(cm.rf)| overall | |
|---|---|
| Accuracy | 0.8647503 |
| Kappa | 0.6011184 |
| AccuracyLower | 0.8594013 |
| AccuracyUpper | 0.8699687 |
| AccuracyNull | 0.7637737 |
| AccuracyPValue | 0.0000000 |
| McnemarPValue | 0.0000000 |
| overall| | |
| |:————–|———:| | |
| |Accuracy | 0.8643818| | |
| |Kappa | 0.6007945| | |
| |AccuracyLower | 0.8590268| | |
| |AccuracyUpper | 0.8696063| | |
| |AccuracyNull | 0.7637737| | |
| |AccuracyPValue | 0.0000000| | |
| |McnemarPValue | 0.0000000| |
CONCLUSIONS:
In this binary context the random forest model performs best to classiy income levels. If the complexity or dimensionality were greater, I would neural neetwork would close the accurscy gap.
The analysis confirmed (and quantified) what is considered common sense:
Age, education, occupation, and marital status (or relationship kind) are good for predicting income (above a certain threshold).
- if a person earns more than $50000 he is very likely to be a married man with large number of years of education;
- single parents, younger than 25 years, who studied less than 10 years, and were never-married make less than $50000.
INFERENCES
About 46% of the people are in a relationship called “Husband” or “Wife” which is then further classified based on Education Level where nearly 14% who earn above $50 K have the education of Bachelors, Prof-school, Masters and Doctorate.
The other education levels have income predominantly below $50 k with just 2% having salaries above $50k who also have capital gains greater than $5096
With respect to other relationships, only 1% have income above $50 k and with capital gains greater than $7074.
In the relationship of Education and Number of People Earning > 50 k and separated by Work Class. We find that Bachelors graduates working in Private companies have a higher number of people earning above 50 k.
In the relationship of Average hours per week with respect to gender and separated by Work Class and we find that Males typically work more hours per week on Average across all work classes.
In the relationship of marital status and income levels separated by Work Class, the majority of the people in Married with Civilian spouse have an income greater than 50 k and majorly in the private sector.
A takeaway in looking at implact of occupation, capital gain and capital loss on the income; we find that Executives at Managerial Level have more people with income greater than 50k and Professional Speciality has more capital gains.